HW #1
ECE 351
Due: February 1st
Spring 2016
1) Consider the coaxial TL shown below. The parameters of the TL are L = 0.8
µH/m, C = 320 pF/m, G = 0 µS/m and R = 0 Ω/m. The source is operating at ω =
6x106 rad/s. If the frequency is 970 KHz determine the characteristic impedance,
propagation constant and phase velocity.
2) The voltage on a transmission line is given as 𝑣(𝑡) = 150 cos(7.5 × 1010 𝑡 −
500𝑥). Determine: (a) the frequency, (b) the phase velocity, (c) the wave-length,
and (d) the phasor expression for 𝑣(𝑡).
3) An infinite transmission line is lossless and has a characteristic impedance of 100
ohms. A signal generator with an internal voltage of 100∠0𝑜 r.m.s. volts and an
internal impedance of 50+j50 ohms is connected to the input of the line.
Determine: (a) the sending end voltage, (b) the sending end current, and (c) the
input impedance, Zs.
4) Two basic equations for a distributed parameter transmission line developed for a
𝜕𝑣
𝜕𝑖
𝜕𝑖
𝜕𝑣
TL have been 𝜕𝑥 = −𝑅𝑖 − 𝐿 𝜕𝑡 and 𝜕𝑥 = −𝐺𝑣 − 𝐶 𝜕𝑡 . If R = 0.053 Ω/m, L = 0.62
𝜕𝑖
µH/m, G = 950 µS/m and C = 39.5 µF/m; determine 𝜕𝑥 at a point 𝑥 on the line
where 𝑣(𝑡) = 60 cos(103 𝑡 + 45𝑜 ). Your answer must be expressed in the form
𝜕𝑖
= 𝐴𝑐𝑜𝑠(𝜔𝑡 ± 𝐵) with 𝐵 in degrees.
𝜕𝑥
5) For a TL with a characteristic impedance of 100 Ω; compute the reflection
coefficient at the load for:
a. 𝑍𝐿 = 50 Ω.
b. 𝑍𝐿 = 100 Ω.
c. 𝑍𝐿 = 0 Ω.
d. An open circuit load.
e. a capacitor with C = 10 pF at 100 MHz.
f. a capacitor having an impedance of –j30 Ω.
g. ZL = 100+j50 Ω.
6) A slotted-line probe is an instrument used to measure the unknown impedance of
a load, ZL. A coaxial slotted line contains a narrow longitudinal slit in the outer
conductor. A small probe inserted in the slit can be used to sample the magnitude
of the electric field, and, hence, the magnitude of the voltage along the TL. By
moving the probe along the length of the slotted line, it is possible to measure
Vmax and Vmin and the distance from the load at which they occur. Then using the
equation for the VSWR we can compute the voltage standing wave ratio. Next,
an unknown load is connected to a slotted line with a characteristic impedance of
50 Ω. If we measure a standing wave ratio of s = 3, determine the unknown load
ZL. The distance between successive voltage minima is 30 cm and the first
voltage minimum occurs at 12 cm from the load.
7) If   0.5  60 and   24 cm, find the locations of the voltage maximum and
minimum nearest to the load.